Ahmed Karim K, Alsahafi Njah A, Ahmed Hamdy M, Boulaaras Salah, Osman M S
Department of Mathematics, Faculty of Engineering, German International University (GIU), New Administrative Capital, Cairo, Egypt.
Mathematics Department, Faculty of Sciences, Umm AI-Qura University, Makkah, 21955, Saudi Arabia.
Sci Rep. 2025 May 16;15(1):17047. doi: 10.1038/s41598-025-00668-1.
This work is a thorough investigation of mathematical modeling with an emphasis on efficiency and performance optimization. Our research is centered on the cubic-quartic nonlinear Schrödinger equation, specifically concerning birefringent fibers exhibiting nonlinearity in the cubic-quintic-septic-nonic continuum. This work makes a unique and significant addition to the field of science. We have obtained a wide range of soliton solutions for cubic-quintic optical solitons in birefringent fibers by using sophisticated mathematical techniques, most notably the modified extended mapping technique. The solitons that fall under these obtained solutions are dark, singular, bright, and combo bright-dark. Besides, we get other exact wave solutions such as singular periodic, exponential, rational, and Weierstrass elliptic doubly periodic solutions. The study presented in this publication is novel and creative, shedding light on how mathematical techniques might improve the functionality and architecture of fiber communication networks. These results are crucial for understanding pulse propagation in birefringent optical fibers governed by the cubic-quartic nonlinear Schrödinger equation, particularly when nonlinear effects extend into the cubic-quintic-septic-nonic continuum. It highlights the innovative nature of our work and highlights the relevance of our results in furthering the science of nonlinear optics and its possible applications in the real world. Graphical depictions of some of the extracted solutions are included to aid readers in physically understanding the obtained solutions' behavior and characteristics.
这项工作是对数学建模的全面研究，重点是效率和性能优化。我们的研究集中在立方 - 四次非线性薛定谔方程上，具体涉及在立方 - 五次 - 七次 - 九次连续统中表现出非线性的双折射光纤。这项工作为科学领域增添了独特而重要的内容。我们通过使用复杂的数学技术，最显著的是改进的扩展映射技术，获得了双折射光纤中立方 - 五次光学孤子的广泛孤子解。这些获得的解所涵盖的孤子包括暗孤子、奇异孤子、亮孤子和亮 - 暗组合孤子。此外，我们还得到了其他精确波解，如奇异周期解、指数解、有理解和魏尔斯特拉斯椭圆双周期解。本出版物中提出的研究新颖且富有创造性，阐明了数学技术如何能够改善光纤通信网络的功能和架构。这些结果对于理解由立方 - 四次非线性薛定谔方程控制的双折射光纤中的脉冲传播至关重要，特别是当非线性效应延伸到立方 - 五次 - 七次 - 九次连续统时。它突出了我们工作的创新性，并强调了我们的结果在推进非线性光学科学及其在现实世界中可能应用方面的相关性。文中包含了一些提取解的图形描述，以帮助读者从物理上理解所获得解的行为和特征。
